For having an intuitive GUI synchronisation client, you may use grsync using a gvfs path on Linux or a Drive Letter on Windows where the WebDAV Storage is preliminary mounted. Or go for the commercial sync tool GoodSync which has WebDAV protocol built-in.

But now, when you try to synchronise with the WebDAV storage (e.g. to OwnSpace Web Storge or to Dropbox), you probably get many "file not found" errors and you end up with no files on the WebDAV storage.

To get that to work, you must use the rsync option "--inplace". Search for rsync options or an option meaning "directly write to files instead of temporary files".